Question

. A convertible moves toward you and then passes you; all the while, its loudspeakers are producing a sound. The speed of the car is a constant 9.30 m/s, and the speed of sound is 342 m/s. What is the ratio of the frequency you hear while the car is approaching to the frequency you hear while the car is moving away

Answer 1

Answer:

$1.056$

Explanation:

v = Velocity of sound = 342 m/s

$v_s$ = Velocity of source of sound = 9.3 m/s

$f_a$ = Frequency when car is approaching

$f_m$ = Frequency when car is moving away

$f_s$ = Frequecy of source of sound

The required ratio is

$\dfrac{f_a}{f_m}=\dfrac{\dfrac{v}{v-v_s}f_s}{\dfrac{v}{v+v_s}f_s}\\\Rightarrow \dfrac{f_a}{f_m}=\dfrac{v+v_s}{v-v_s}\\\Rightarrow \dfrac{f_a}{f_m}=\dfrac{342+9.3}{342-9.3}\\\Rightarrow \dfrac{f_a}{f_m}=1.056$

The ratio of the frequency you hear while the car is approaching to the frequency you hear while the car is moving away is $1.056$